A mortarless masonry structure comprising a plurality of regular masonry blocks and/or bricks connected to each other by a plurality of metal bars and a plurality of standard metal threaded fasteners thereby forming a post tensioned structure. Preferably, the blocks are operatively connected to each other as a structure by simple mechanical tools. Each interconnection results in a unitized post tensioned member that, when interconnected to the adjacent members, forms a comparatively higher strength structure than systems made of mortar and reinforced mortar. The method used to create this structure is a simple, waterless, mortarless interconnection process that is completed by a series of simple individual steps of fastening the blocks and bars into a strong and durable structure. Once connected the structure is strong and durable. If desired, the structure may be disassembled and the components re-used.